What are all the solutions?

4x^2+9y^2=72

x - y 2 = - 1

Given:

4x^2+9y^2=72 ... (1)

Assuming the second equation is

x-y^2=-1 ... (2)

Rewrite (2) as y^2=x+1 ... (2a)

and substitute in (1)

4x^2+9 (x+1) = 72 = >

4x^2+9x-64=0 ... (3)

Solve (3) by quadratic formula:

x = (-9 ± √ (1105)) / 8

={-5.280, 3.030} [ to three places after decimal ]

Substitute in (2a) to solve for y.

y = ± sqrt (-4.280) or ± sqrt (4.030) or

y = ± 2.0689i and ± 2.0075

ALL four solutions are: { (-5.2802,2.0689i), (-5.2802,-2.0689i), (3.0302,2.0075), (3.0302,-2.0075) }, two of which are complex.

If we reject complex roots

we are left with the real solutions { (3.0302, 2.0075), (3.0302, - 2.0075) }